Spatial Understanding Vantage Point

As discussed earlier and as illustrated in Figure 12.2, any given representation has a particular vantage point that is determined by the combination of viewing distance, viewing angle, and viewing azimuth. Our empirical work has addressed children's developing appreciation of vantage point by examining their ability to distinguish among images that depict the same referent from different vantage points, and to produce representations that fit certain vantage-point specific qualities.

As one means of testing children's appreciation of the elements of vantage point shown in Figure 12.2, we (Liben & Szechter, 2001) prepared pairs of photographs with the same referent. Children were shown each pair of photographs and asked whether they were identical. Whenever children judged the photographs to be different, they were asked to say whether the photographs differed because something had changed in the scene itself, or because of something that had been done by the person who took the photograph. Irrespective of which attribution was given, the child was asked to explain what had happened, that is, what had changed, or what the photographer had done. Critical items were 15 pairs in which the photographer's vantage point had changed by altering viewing distance, viewing angle, or viewing azimuth (illustrated in Figure 12.4). To ensure that correct answers varied, there were also filler items in which either something in the scene had changed or in which the photographs were identical.

This spatial photo-pair task was given to children aged 3-, 5-, and 7-years, as well as to a comparison group of college students. For pairs that differed by viewing distance (so that a correct response would include explaining that the photographer had moved closer to, or further away from the depicted subject), only about 25% of the 3-year-old children were correct even on a single one of the five items; the rest were completely unable to explain anything about viewing distance. About 50% of the 5-year-old children were correct on four or all five items, with the rest distributed fairly evenly across the remaining lower scores; just over 75% of the 7-year-old children were correct on all or all but one items, and virtually all adults had errorless performance.

For pairs that differed by viewing angle or viewing azimuth, the pathway to mastery was more protracted. More specifically, for viewing-angle pairs, none of the 3-year-old children explained even a single item. Indeed, children of this age commonly failed to even notice that anything differed in the two photographs, focusing instead on the shared referential content. For example, when commenting on the viewing-angle pair (tulips) shown in Figure 12.4, one 3-year-old child said, "They're both the same." When the interviewer continued by saying, "Well, they're both of tulips, but is there anything different about the pictures?" the child answered in the negative, saying, "Nope. This one [pointing to one on the right] has the same stuff."

The 5-year-old children were more likely to notice a difference between the two images, but their explanations suggested they inferred that there had been a change in what had been in the scene rather than in the way that was photographed. Thus, for example, 5-year-olds accounted for the difference

between the tulip photographs by explaining that the photographer took "this one when [the tulips] were all curled up and those ones when they were all blooming," that the photographs were taken "in the spring [when] they were closed [and] then in the summer [when] they came out again," and that the photographer "took one sometime when they were closed and one sometime when they were open." About half of the 5-year-old children were able to provide correct explanations of at least one angle pair, sometimes extremely clearly as one child explained, "Um, that one you're looking that way [points straight ahead] and that one you're looking down, this way [bends over the picture]" or another who said, "Oh I like these . . . He [the photographer] went sort of on the side of them and then like up above them to get the middle [points hand down on top of the tulips and rises in chair] . . . because um, like this one is like straight across and this one's like you're looking down [flexes hand to point all fingers down onto the tulips]." By the age of 7, responses like these were common, and by adulthood, they were virtually universal.

The azimuth pairs showed an even more protracted period for mastery. Again, many 3-year-old children failed to note the difference between the two photographs, but even when they did, they commonly believed that there had been a change in the referent objects rather than a change in the photographer's position. To illustrate by reference to the rooster-tile azimuth example shown in Figure 12.4, many children (and even some adults) thought that what had changed was the orientation of the tile rather than the vantage point of the photographer. That it was, instead, the photographer's position that had changed is apparent from looking at the grain pattern of the wood surface on which the tile rests.

In a second task used to study the developing ability to understand vantage point, we gave digital cameras to 8- to 10-year-old children and adults, and asked them to reproduce model photographs. Specifically, respondents were asked to "try to take a picture so that yours will look as much like this photograph as you can make it" and then, after viewing the result on the display screen of the digital camera, to take a second photograph to try to improve the match. Figure 12.5 shows a sample of children's initial photographs for one model. Photographs were scored by assigning points to qualities of the photograph that reflected correct viewing distance, viewing angle, and viewing azimuth. An analysis of variance on scores totaled over four photographs revealed significant effects of age and trial, and a significant interaction showing that the improvement over trials was significant in children only.

We also studied understanding of vantage point by asking participants to create photographs that were consistent with some view-specific verbal description. For example, as participants approached an art museum at which two lion paw sculptures flanked the entrance they were asked to take a photograph with "just one paw in the picture." Adults were almost universally successful in implementing this request, usually by adjusting the direction the camera pointed (azimuth). Only 10% of the adult participants produced an image in which a second paw showed at the edge of the image, an error presumably accounted for by the fact that the area recorded on the image is slightly larger than that

Figure 12.5 Four sample responses to a request to reproduce a photographic model that was almost identical to the bottom right photograph. Reproduced from Liben (2003a) with permission.

Figure 12.6 Illustrative responses by children asked to create a photograph showing only one paw. Solutions involved (1) canonical azimuth (front view) but noncanonical distance (close up), (2) nonca-nonical azimuth (building entrance viewed from side), (3) noncanonical azimuth (back view), (4) non-canonical distance and azimuth (close and to the side), (5) noncanonical angle (overhead rather than eye-level), and (6) change in referent (child said he "waited for people walking by to block one of the paws from view.") Reproduced from Liben (2003a) with permission.

seen through the viewfinder. Errors were more common (32%) among children. Unlike adults, when children erred, the second paw typically appeared well within the frame of the image. The children who were successful used a variety of strategies involving distance, angle, and azimuth as illustrated in Figure 12.6.

Another way that we have studied the developing ability to understand the spatial meaning contained in graphic representations is to ask participants to transfer location or direction information gleaned from one spatial-graphic representation to another. Table 12.4 lists four representation-to-representation tasks discussed next. In each, participants were first given some kind of representation (such as an eye-level photograph, aerial photograph, or line drawing) of a space (such as a park, city, or local region) that was not currently in view. They were then asked to demonstrate their understanding of some information that could be gleaned from that representation (e.g., the location of a particular landmark in the represented park) by performing some task on another representation of that same referent space (e.g., placing a location dot on a plan map of the park). Success on tasks like these draws simultaneously and interactively on understanding the initial depiction (e.g., the eye-level photograph), on understanding of the representation on which responses must be made (e.g., the plan map), and on the skill (and care) needed to implement the required response (e.g., precision in placing the sticker on the plan map to show the landmark's location).

In the city aerial task (Liben & Downs, 1991), first and second graders were given individual copies of an aerial photograph of Chicago. After class discussion of the photograph and its general referent, children were asked to use it as a basis to draw (but not trace) a map of Chicago. Next, children were given a plan map, and were asked to identify what area of the photograph was depicted. An acetate sheet was then placed over each child's copy of the aerial photograph to outline the correct area and to